The present disclosure is generally related to the field of color image/text printing or display systems and to methods and systems for calibrating color output devices, such as color displays, printers and printing devices thereof. Color has become essential as a component of communication and facilitates the sharing of knowledge and ideas, and there are continuous efforts to improve the accuracy and total image quality of digital color output devices. Color images are commonly represented as one or more separations, each including color density signals for a single primary or secondary color. Color density signals are commonly represented as digital gray or contone pixels, varying in magnitude from a minimum to a maximum, with a number of gradients between corresponding to the bit density of the system, where a common 8-bit system provides 256 shades of each primary color. A color can therefore be considered the combination of magnitudes of each pixel, which when viewed together, present the combination color, with color printer signals typically including three subtractive primary color signals Cyan (C), Magenta (M), and Yellow (Y) and a Black signal (K), which together can be considered the printer colorant signals. Each color signal forms a separation and when combined together with the other separations, forms the color image. Color images, text, and other features in a given document or print job are generally specified as image data in a printer-independent form (color space) based on the characteristics of human vision to facilitate the exchange and reuse of documents.
The native control spaces of output devices in a printing system, however, are not printer-independent color spaces. Consequently, printing systems are characterized and calibrated by determining the device control values corresponding to specified printer-independent color values in order to print a given color. This is normally accomplished by a three-step procedure. Initially, a set of color patches with pre-determined device control values is output on the device and the color of each patch is measured in printer-independent color coordinates. This may include printing test patches on a sheet of paper and measuring the resulting patch colors or transferring toner or other marking material onto an intermediate medium (e.g., an intermediate transfer belt or photoreceptor in the system) and measuring the color of the transferred material. Next, a “forward device-response function” or forward transform is estimated using the device control values and the corresponding measured printer-independent color values, sometimes referred to as a measured toner response curve (TRC), which represents a mapping from device control values to the printer-independent-color values produced by the device in response to the control values. The forward response function is then inverted to obtain a “device-correction-function” or inverse transform that maps each printer-independent color to the device control values that produce the specified printer-independent color value on the output device, and this is stored in the printer. In operation, the printer-independent color values of a given print job are mapped through the “device correction-function” to obtain control values that are used by the rendering devices of the printer to produce the desired color. By this process, the printing system transfer function from input (device-independent) data to output (printed media) is calibrated and essentially linearized. An example of a calibration system is described in U.S. Pat. No. 5,305,119 to Rolleston et al, “Color Printer Calibration Architecture,” which issued on Apr. 19, 1994 and is assigned to Xerox Corporation, and which is generally directed toward a method of calibrating a response of a printer to an image described in terms of calorimetric values. Another example of a calibration method and system is described in U.S. Pat. No. 5,528,386 to Rolleston et al, “Color Printer Calibration Architecture”, which issued on Jun. 18, 1996 and is also assigned to Xerox Corporation, and which describes a conventional one-dimensional architecture. Both U.S. Pat. Nos. 5,305,119 and 5,528,386 are incorporated herein by reference.
Calibration and/or characterization of color printers is often subject to different forms of noise. In particular, digital correction of a printer TRC often requires measuring points along the TRC, and then projecting, for each desired density, how many pixels must be turned on to achieve that density. Typically a few points along the TRC are measured and a line is fit through the measured points using linear interpolation or other curve fitting techniques, or a parameterized function may be fit to the measured data. Conventional spline fitting can leave the fit too sensitive to measurement noise, which can induce contours. Parameterized functions are typically not flexible enough to cover the full range of TRC variation observed. Consequently, there remains a need for improved printing system calibration and characterization techniques to better fit measured TRCs to avoid or mitigate the effects of measurement noise while accurately characterizing the true machine performance.